Almost two-thirds of Republicans oppose the Supreme Court’s backing of gay marriage, according to a Reuters/Ipsos poll, which gives hope for conservative presidential candidates who have come out strongly against marriage equality.

Republicans would struggle to make opposition to same-sex marriage a winning issue in next November’s general election because more than half of Americans support it, according to the online survey.

That could give a boost to gay marriage opponents like Wisconsin Gov. Scott Walker, Sen. Ted Cruz of Texas and former Arkansas Gov. Mike Huckabee in the fight for the Republican nomination.

Walker, whose is widely expected to declare his candidacy next week, described the Supreme Court ruling as a “grave mistake,” and has called for a constitutional amendment to allow states to decide whether to allow gay marriage.

Forty-two percent of Republicans in the poll said same-sex marriage laws should be made at the state level by referendum, a view taken by only 24 percent of the overall population.

Cruz has vowed to put his opposition to gay marriage “front and center” of his campaign and has urged some states to ignore the court ruling. Huckabee has long been a vocal opponent of gay rights.

Their positions might appeal to the kind of older, conservative Republican who turns out to vote in the Iowa caucuses, the first nominating contest in the 2016 White House race, said University of Northern Iowa political science professor Christopher Larimer.

“Part of it’s a generational thing,” Larimer said.

Other leading Republican candidates like former Florida Gov. Jeb Bush and Sen. Marco Rubio of Florida have voiced support for traditional marriage but shied away from strong criticism of the Supreme Court.

When asked in general whether they support allowing same-sex couples to marry, 51 percent of Americans say they do, while 35 percent oppose it. Forty-eight percent of independent voters back gay marriage, making it difficult for a conservative Republican to win general election votes on the issue.

The poll was conducted between June 26 and July 8 among 3,632 people.

Reuters/Ipsos online polls are measured with a credibility interval. Among all respondents, the gay marriage poll had an overall credibility interval of plus or minus 1.9 percentage points, and plus or minus 3.3 percent for Republican respondents.